问题标题:
Gmat数学,求简便算法~~Foreveryintegerkfrom1to10,inclusive,thekthtermofacertainsequenceisgivenby.IfTisthesumofthefirst10termsinthesequence,thenTis(A)greaterthan2(B)between1and2(C)between1/2and1(D)
问题描述:
Gmat数学,求简便算法~~
Foreveryintegerkfrom1to10,inclusive,thekthtermofacertainsequenceisgivenby.IfTisthesumofthefirst10termsinthesequence,thenTis
(A)greaterthan2
(B)between1and2
(C)between1/2and1
(D)between1/4and1/2
(E)between1/4
thekthtermofacertainsequenceisgivenby(-1)^(k+1)乘以(1/2^k)
黄伟平回答:
答案选D,解法如下:
thekthtermofacertainsequenceisgivenby(-1)^(k+1)乘以(1/2^k)
说明通项公式为:an=(-1)·(-1/2)^k
又因为K=10,已经是一个较大的数了,1-q^n,在n较大的情况下,是可以忽略的,因此
sn=a1/(1-q),代入即为:1/2除以1-(-1/2),答案为1/3.
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